Digital to analog converters (DAC) are commonly used analog blocks, which play an important role of converting a value in the digital domain to a value in the analog domain. Generally, DACs can be characterized into two groups. The first group includes DACs that operate at Nyquist rate (hereinafter referred to as “Nyquist DACs”), which is twice the maximum input signal frequency, allowing the input signal to be recovered without distortion. The second group of DACs include DACs that operate at a sampling rate higher than the Nyquist rate (hereinafter referred to as “oversampled DACs”). Oversampled DACs can achieve higher resolution without increasing complexity; however, this increased resolution comes at decreased conversion rate. This is because a more precise value is generated through the process of averaging over time. As an example, 0.5 LSB can be produced by putting out a 1 followed by a zero which averages to 0.5 over two time steps. However, the added resolution in the example is achieved by trading time and the cost is that the DAC can only provide this extra resolution to input signals with half the Nyquist rate.
A common implementation of DAC uses an array of current sources, which are selectively turned on to create an analog output proportional to the magnitude of the digital value. Some exemplary implementations of such DACs include current-steering DACs, switched-capacitor DACs and resistor-string DACs. However, due to practical limitations (e.g. manufacturing), systematic errors are introduced into the conversion. One example of such systematic errors is gradient error created by inconsistencies in the silicon wafer, including thermal, doping and oxide thickness gradients. This can cause component properties to vary along a particular direction. Since DACs are built through arraying identical devices in two dimensions, the output produced by different components exhibit the same gradient in their current/voltage output. The result is that the output of the array of current sources is non-linear, leading to Integral Non-Linearity (INL) and Differential Non-Linearity (DNL).
There are known ways to cope with INL and DNL. One commonly used technique is to randomize the selection of the current sources to improve the INL and DNL. Other techniques include reordering the selection of the current sources in an effort to cancel out the effects of gradient errors, thus improving INL and DNL, and using a separate calibration DAC that uses a look-up table to produce a compensating current that cancels out the systematic effects of INL and DNL. However, these known techniques require an additional DAC which must now produce the exact compensation which is somehow characterized over a large number of DACs, averaged and represented as look-up table (LUT) entries. These entries apply to all the DACs over process and temperature corners and produce limited compensation ability. The compensating DAC and the associated LUT also take up space and current consumption and provide compensation ability to the extent of applicability of the calibration values.
Another widely used approach provides the compensation by alternating the selection of next current cell elements such that the gradient is cancelled by inherent selection of successive devices. As input is increased the gradient is cancelled by choosing next addressed element to be on the opposite side of the gradient. However, this method requires the knowledge of gradient a priori in order to device a scheme of switching selection. This is unfortunate if the expected gradient turns out to be different than the actual gradient as the scheme will no longer provide the intended correction. Also, if the gradient changes from one lot to another or from one fabrication plant to another, there is no efficient way of determining a compensation scheme that would work across all the devices since the solution is hard-wired.
Accordingly, a DAC that addresses at least some of these disadvantages is highly desirable.
It will be noted that throughout the appended drawings, like features are identified by like reference numerals.